All other things being equal Halachically, if you have two people with Yahrtzeits one for a mother and one for a father, who has priority with regards to getting an Aliyah (and/or davening for the amud and/or saying kadish), and why?

2 Answers
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The halacha does not differntiate between one mourning for a mother or a father in terms of priority for any of the chiyuv davening activities. In fact, Kitzur Shulchan Aruch 26:16 states that even one who is mourning for both a mother and a father does not get priority over one mourning for another relative.

From sefer shraga hameir the one after the father has precedence. Since the father needs more zechusim in the next world since he had a harder time in this world. He has more mitsvot to keep and his yetser hora in sexual matters is a lot stronger like MZL which a woman does not have.